This paper illustrates a different conception of arithmetic, an arithmetic with reasons as well as rules. This arithmetic includes making connections between different representations and making sense of rules as well as using them. It provides a foundation for "Algebra the Web of Knowledge and Skill" in the sense that algebra can be seen as the generalization, formalization, and symbolization of this arithmetic. Past and recent views of arithmetic are contrasted in order to make the differences between them explicit. Arithmetic yet to come is also considered. (Contains 27 references.) (ASK)

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